В прямоугольном треугольнике со сторонами: a = 0.5053, b = 0.475, с = 0.6935 высота равна h = 0.3461
Ответ:
a=0.5053
b=0.475
c=0.6935
α°=46.77°
β°=43.23°
S = 0.12
h=0.3461
r = 0.1434
R = 0.3468
P = 1.674
Решение:
Гипотенуза:
c =
b
cos(α°)
=
0.475
cos(46.77°)
=
0.475
0.6849
= 0.6935
Угол:
β° = 90°-α°
= 90°-46.77°
= 43.23°
Высота :
h = b·sin(α°)
= 0.475·sin(46.77°)
= 0.475·0.7286
= 0.3461
Катет:
a = h·
c
b
= 0.3461·
0.6935
0.475
= 0.5053
или:
a = √c2 - b2
= √0.69352 - 0.4752
= √0.4809 - 0.2256
= √0.2553
= 0.5053
или:
a = c·sin(α°)
= 0.6935·sin(46.77°)
= 0.6935·0.7286
= 0.5053
или:
a = c·cos(β°)
= 0.6935·cos(43.23°)
= 0.6935·0.7286
= 0.5053
или:
a =
h
cos(α°)
=
0.3461
cos(46.77°)
=
0.3461
0.6849
= 0.5053
или:
a =
h
sin(β°)
=
0.3461
sin(43.23°)
=
0.3461
0.6849
= 0.5053
Площадь:
S =
h·c
2
=
0.3461·0.6935
2
= 0.12
Радиус описанной окружности:
R =
c
2
=
0.6935
2
= 0.3468
Радиус вписанной окружности:
r =
a+b-c
2
=
0.5053+0.475-0.6935
2
= 0.1434
Периметр:
P = a+b+c
= 0.5053+0.475+0.6935
= 1.674